A theory of bidirectional solitons on water is developed by using an integrable Boussinesq surface-variable equation. We present an explicit transformation between the system and a member of the Ablowitz-Kaup-Newell-Segur system, and derive an exact multisoliton solution by using a Darboux transformation. The phase shifts and the maximum wave heights during the interaction are studied for two-soliton overtaking and head-on collisions. They agree with the Korteweg-de Vries solution for overtaking collision and the perturbation solution for head-on collision.
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Zhang et al. (2003) studied this question.
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